Building Contractor's Coastal Land Investment Decision
A. What is the contractor’s expected wealth if he purchases the land?
B. What is the contractor’s expected utility from purchasing the land?
C. What is the contractor’s utility if he does not purchase the land? Will the contractor purchase the land? Explain, including a discussion of his risk preference.
D. On a separate scrap sheet, show graphically the contractor’s utility function, including his expected utility if he purchases the land, and his utility if he does not. LABEL CAREFULLY.
E. What would the probability that the land is declared within the "set-back line" have to be in order for the contractor to be indifferent about purchasing the land (in percent)?
A. The contractor's expected wealth if he purchases the land is $676,000.
B. To calculate the expected utility, we multiply the utility of each outcome by its respective probability and sum them up:
C. The utility if he does not purchase the land is $810,000. To determine whether the contractor will purchase the land, we compare the expected utility of purchasing ($676,000) with the utility of not purchasing ($810,000).
D. Please refer to the graph below.
E. To find the probability that would make the contractor indifferent about purchasing the land, we set the expected utility of purchasing equal to the utility of not purchasing and solve for the probability.
In making the decision whether to purchase the coastal land for building a retirement cottage, the building contractor needs to consider his expected wealth, expected utility, and potential risks involved. By analyzing the probabilities and outcomes, the contractor can make an informed decision based on his risk preferences.
The expected wealth if the contractor purchases the land is $676,000, considering the probabilities of the land being designated within the "set-back line." This calculation takes into account the potential scenarios and their respective values.
To determine the expected utility from purchasing the land, the contractor can multiply the utility of each outcome by its probability and sum them up. This calculation provides insight into the overall satisfaction or benefit the contractor may derive from the investment.
If the contractor chooses not to purchase the land, his utility would be $810,000. By comparing this utility with the expected utility of purchasing the land, the contractor can assess whether the investment aligns with his risk preferences and financial goals.
Graphically representing the contractor's utility function can visually illustrate the potential outcomes and assist in decision-making. By labeling the expected utility if he purchases the land and the utility if he does not, the contractor can visually compare the two scenarios.
To achieve indifference about purchasing the land, the contractor needs to determine the probability that would make the expected utility of purchasing equal to the utility of not purchasing. By solving for this probability, the contractor can identify the threshold at which the investment becomes equally favorable or unfavorable.